Quantum randomness
| dc.contributor.advisor | Tame, M. S. | |
| dc.contributor.advisor | Bosman, G. W. | |
| dc.contributor.author | Strydom, Conrad | en_ZA |
| dc.contributor.other | Stellenbosch University. Faculty of Science. Dept. of Physics. | en_ZA |
| dc.date | 2023-02-23T06:09:14Z | |
| dc.date | 2023-08-30T13:05:04Z | |
| dc.date | 2023-02-23T06:09:14Z | |
| dc.date | 2023-08-30T13:05:04Z | |
| dc.date | 2023-03 | |
| dc.date.accessioned | 2023-08-31T09:18:46Z | |
| dc.date.accessioned | 2023-02-23T06:09:14Z | |
| dc.date.available | 2023-08-31T09:18:46Z | |
| dc.date.available | 2023-02-23T06:09:14Z | |
| dc.date.issued | 2023-03 | |
| dc.description | Thesis (MSc)--Stellenbosch University, 2023. | en_ZA |
| dc.description.abstract | ENGLISH ABSTRACT: Randomness is a vital resource with many important applications in information theory. In particular, random numbers play a ubiquitous role in cryptography, simulation and coordination in computer networks. When ran- domness is generated using classical techniques, the unpredictability relies on incomplete knowledge which can introduce ordered features and compromise the application. This thesis explores the use of quantum techniques to generate true randomness and its application to quantum computing. The analogue of random numbers in quantum information are random unitary operators sampled from the uniform Haar ensemble, which are used in a number of quantum protocols. Unfortunately, these cannot be generated efficiently and so pseudorandom ensembles called unitary t-designs are frequently used as a substitute. In the first part of this thesis we investigate t-designs realised using a measurement-based approach on IBM quantum computers. In particular, we implement an exact single-qubit 3-design on IBM quantum computers by performing measurements on a 6-qubit graph state. We show that the ensemble of unitaries realised was a 1-design, but not a 2-design or a 3-design under the test conditions set, which we show to be a result of depolarising noise. We obtain improved results for the 2-design test by implementing an approximate 2-design, which uses a smaller 5-qubit graph state, but the test still does not pass for all states due to noise. To obtain a theoretical understanding of the effect of noise on t-designs, we investigate the effect of various noise channels on the quality of single-qubit t-designs. We show analytically that the 1-design is affected only by amplitude damping, while numeric results obtained for the 2-, 3-, 4- and 5-design suggest that a 2t-design is significantly more sensitive to noise than a (2t − 1)-design and that, with the exception of amplitude damping, a (2t + 1)-design is as sensitive to noise as a 2t-design. Next, we test our approximate measurement-based 2-design on an important application in quantum com- puting, namely noise estimation. For this, we propose an interleaved randomised benchmarking protocol for measurement-based quantum computers that can be used to estimate the fidelity of any single-qubit measurement- based gate. We demonstrate our protocol on IBM quantum computers by estimating the fidelity of a universal single-qubit gate set using graph states of up to 31 qubits. Estimated gate fidelities show good agreement with those calculated from process tomography, which shows that our approximate measurement-based 2-design is of sufficient quality for use in randomised benchmarking, despite not passing our test for all states. While IBM quantum computers provide a sophisticated platform for randomness generation, they are not specifically designed for this task. We therefore investigate randomness generation on custom-built hardware, by integrating an on-chip nanowire waveguide into an optical time-of-arrival based quantum random number generation setup. Despite loss, we achieve a random number generation rate of 14.4 Mbits/s. The generated bits did not require any post-processing to pass industry standard tests. Our experiment demonstrates an order of magnitude increase in generation rate and decrease in device size compared to previous studies. | en_ZA |
| dc.description.abstract | AFRIKAANSE OPSOMMING: Willekeurigheid is ’n noodsaaklike hulpbron met vele belangrike toepassings in inligtingsteorie. Lukrake getalle speel veral ’n alomteenwoordige rol in kriptografie, simulasie en koördinasie in rekenaarnetwerke. So- dra willekeurigheid deur klassieke tegnieke gegenereer word, steun die onvoorspelbaarheid op onvolledige kennis wat geordende kenmerke kan meebring en die toepassing skaad. Hierdie tesis ondersoek die gebruik van kwantum tegnieke om ware willekeurigheid te skep, asook die toepassing daarvan in kwantum berekeninge. In kwantum inligting stem lukrake getalle ooreen met lukrake eenheidsoperatore gesteekproef vanuit die eenvormige Haar-samevatting wat in ’n aantal kwantum protokolle gebruik word. Ongelukkig kan hierdie nie doeltreffend geskep word nie en dus word pseudo-lukrake samestellings genaamd eenheids-t-ontwerpe, gereeld as plaasvervangers gebruik. In die eerste gedeelte van hierdie tesis ondersoek ons t-ontwerpe gerealiseer deur ’n metings-gebaseerde benadering op IBM kwantum rekenaars. In besonder, implementeer ons ’n presiese enkel- kubit 3-ontwerp op IBM kwantum rekenaars deur metings uit te voer op ’n 6-kubit grafiektoestand. Ons toon dat die samestelling van eenheidsoperatore wat gerealiseer is, ’n 1-ontwerp, maar nie ’n 2-ontwerp of 3-ontwerp onder die vasgestelde toetstoestande is nie, vanweë depolariserende geraas. Ons bekom verbeterde resultate vir die 2-ontwerp toets deur implementering van ’n benaderde 2-ontwerp, wat ’n kleiner 5-kubit grafiektoestand benut, maar die toets slaag weens geraas steeds nie vir al die toestande nie. Om ’n teoretiese begrip van die invloed van geraas op t-ontwerpe te verkry, ondersoek ons die invloed van verskeie geraaskanale op die kwaliteit van enkel-kubit t-ontwerpe. Ons toon analities dat die 1-ontwerp slegs deur amplitude demping geraak word, terwyl numeriese resultate verkry vir die 2- , 3- , 4- en 5-ontwerp aandui dat ’n 2t-ontwerp aansienlik meer sensitief is vir geraas as ’n (2t − 1)-ontwerp en dat, met uitsondering van amplitude demping, ’n (2t + 1)-ontwerp ewe sensitief is vir geraas as ’n 2t-ontwerp. Ons toets volgende ons benaderde metings-gebaseerde 2-ontwerp op ’n belangrike toepassing in kwantum berekeninge, naamlik geraasskatting. Hiervoor stel ons ’n tussengelaagde lukrake peilmerking protokol vir metings-gebaseerde kwantum rekenaars voor wat gebruik kan word om die betroubaarheid van enige enkel- kubit metings-gebaseerde poort te skat. Ons demonstreer ons protokol op die IBM kwantum rekenaars deur die betroubaarheid van ’n universele enkel-kubit poort-stel te skat deur gebruik te maak van grafiektoestande van tot 31 kubits. Geskatte poort-betroubaarhede toon goeie ooreenkoms met dié bereken van prosestomografie, wat toon dat ons benaderde metings-gebaseerde 2-ontwerp van voldoende gehalte is vir gebruik in lukrake peilmerking, alhoewel dit nie ons toets vir alle toestande slaag nie. Alhoewel IBM kwantum rekenaars ’n gesofistikeerde platform vir die skepping van willekeurigheid ver- skaf, is hulle nie spesifiek vir hierdie doel ontwerp nie. Ons ondersoek dus die skepping van willekeurigheid op doelgerigte hardeware, deur ’n op-skyfie nanodraad golfgids te integreer met ’n optiese aankomstyd-gebaseerde kwantum lukrake getal-skeppende stelsel. Ondanks verlies, behaal ons ’n lukrake getalskeppingstempo van 14.4 Mbits/s. Die gegenereerde binêre syfers het geen verdere verwerking vereis om aan nywerheidstandaarde te voldoen nie. Ons eksperiment demonstreer ’n grootte-orde toename in die skeppingstempo en afname in toestel-grootte vergeleke met vorige studies. | af_ZA |
| dc.description.version | Masters | |
| dc.embargo.terms | 2023-09-01 | |
| dc.format | application/pdf | |
| dc.format.extent | xvii, 114 pages : illustrations (some color) | en_ZA |
| dc.identifier | http://hdl.handle.net/10019.1/127432 | |
| dc.identifier.uri | https://scholar.sun.ac.za/handle/10019.1/128459 | |
| dc.language | en_ZA | |
| dc.publisher | Stellenbosch : Stellenbosch University | en_ZA |
| dc.rights.holder | Stellenbosch University | en_ZA |
| dc.subject.lcsh | Quantum computing -- Mathematical models | en_ZA |
| dc.subject.lcsh | Quantum information processing | en_ZA |
| dc.subject.lcsh | Information theory in physics | en_ZA |
| dc.subject.lcsh | Quantum cryptography | en_ZA |
| dc.subject.lcsh | Computer networks -- Security measures | en_ZA |
| dc.subject.name | UCTD | en_ZA |
| dc.title | Quantum randomness | en_ZA |
| dc.type | Thesis |
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